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DEPARTMENT  OF  THE  INTERIOR 


UNITED  STATES  GEOLOGICAL  SURVEY 

GEORGE  OTIS  SMITH,  Director 


Bulletin  344 


THE 


RESULTS  OF  TESTS  OF  108  BEAMS 

^FIRST  SERIES) 

MADE  AT  THE  STRUCTURAL-MATERIALS 
TESTING  LABORATORIES 


By  RICHARD  L.  HUMPHREY 


WASHINGTON 

GOVERNMENT  PRINTING  OFFICE 

1908 


✓ 


(oZOA 

H  ■ 


•  I 

CONTENTS. 

-*  > 

< 


• 

Page. 

Introduction . 

.  5 

Scope  of  investigations . 

.  5 

Methods  of  testing . 

. .  6 

• 

Results  of  tests . 

.  6 

Acknowledgments . . 

.  8 

Tests  of  constituent  materials . 

.  9 

Cement . . . 

.  9 

Preparation  of  typical  cement . 

.  9 

Results  of  tests . . 

.  9 

Sand . . . 

.  16 

Aggregate . 

. 18 

Preparation  of  test  pieces . 

. . .  18 

Methods  of  proportioning . 

18 

Method  of  mixing  and  consistency. . _ 

-  - . - —  - 

vr:V.r.:.  -  19 

i 

Mixing . 

.  19 

Consistency . 

.  20 

Method  of  molding . 

.  21 

Beams . 

.  21 

ft 

Cylinders  and  tubes . 

-  .  =  ^r-. . 

.  21 

Moving  and  storage . 

.  22 

Methods  of  testing . 

. ....;. . . .  22 

Beams . 

. . .  22 

v 

Long  beams .  . 

.  22 

Apparatus . 

.  .  22 

Method  of  zero  deformation . . . . 

.  23 

• 

Method  of  testing . 

. .  27 

— 

Short  beams . 

27 

Cylinders  and  cubes . 

. .  28 

c* 

Results  of  tests . 

. .  28 

Beams  of  constant  span . 

. . .  28 

■9 

Beams  of  variable  span . 

. . . !. . .  55 

ci 

Cylinders  and  cubes . 

. . .  55 

A 

Illustrative  diagrams . 

. . . .  57 

A  f  .  | 

Survey  publications  on  tests  of  structural  materials . . . .  59 


0 49559 


4 


ILLUSTRATIONS. 


Page. 

Plate  I.  Concrete  beam  in  machine  ready  for  testing .  22 

Fig.  1.  Diagrams  illustrating  method  for  computation  of  concrete  beams .  25 

2.  Effect  of  age  and  consistency  on  the  strength  of  cinder  concrete .  28 

3.  Effect  of  age  and  consistency  on  the  strength  of  granite  concrete .  29 

4.  Effect  of  age  and  consistency  on  the  strength  of  gravel  concrete . .  29 

5.  Effect  of  age  and  consistency  on  the  strength  of  limestone  concrete _  30 

6.  Compression-stress  deformation  diagrams  of  cinder  concrete .  30 

7.  Compression-stress  deformation  diagrams  of  granite  concrete .  31 

8.  Compression-stress  deformation  diagrams  of  gravel  concrete .  32 

9.  Compression-stress  deformation  diagrams  of  limestone  concrete .  33 

10.  Deformation  curves  of  cinder  concrete  in  flexure .  35 

11.  Deformation  curves  of  granite  concrete  in  flexure .  54 

12.  Deformation  curves  of  gravel  concrete  in  flexure .  56 

13.  Deformation  curves  of  limestone  concrete  in  flexure.. . . .  58 

% 


TABLES. 


Page. 

Table  1.  Chemical  analyses  of  the  individual  brands  used  in  the  preparation 

of  typical  Portland  cement . . .  10 

2.  Physical  tests  of  individual  brands  of  cement .  10 

3.  Strength  tests  of  individual  brands  of  cement .  11 

4.  Physical  properties  of  cements  used  in  concrete  beams .  14 

5.  Mortar  tests  of  Meramec  River  sand  used  in  concrete  beams .  17 

6.  Physical  properties  of  sand  and  other  materials  forming  aggregates. .  17 

7.  Strength  tests  of  cement  (Ct.  140)  used  in  testing  Meramec  River 

sand .  18 

8.  Tests  of  13-foot  concrete  beams  of  constant  (12-foot)  span;  ages  4, 

13,  and  26  weeks .  36 

9.  Tests  of  concrete  beams  of  variable  span;  ages  4,  13,  and  26  weeks. .  42 

10.  Compression  tests  of  concrete  cylinders  and  cubes  accompanying 

beams;  ages  4,  13,  and  26  weeks .  48 

4 

W 


t- 


THE  STRENGTH  OF  CONCRETE  BEAMS. 


By  Richard  L.  Humphrey. 


INTRODUCTION. 

SCOPE  OF  INVESTIGATIONS. 

The  tests  of  concrete  beams  described  in  this  bulletin  form  a  part 
of  a  comprehensive  series  of  investigations  undertaken  by  the  United 
States  Geological  Survey  for  the  purpose  of  determining  the  strength 
of  concrete  and  reinforced  concrete. 

The  work  involved  in  these  investigations  consists  of  a  study 
(1)  of  the  constituent  materials  of  concrete,  (2)  of  its  strength  when 
molded  into  various  structural  shapes,  and  (3)  of  the  methods  by 
which  its  maximum  strength  may  be  developed  through  various 
forms  of  metallic  reinforcement. 

Although  it  is  true  that  concrete  possesses  but  little  strength  in 
tension  and  must  be  reinforced  with  metal  to  resist  tensile  stresses, 
it  is  believed  that  no  study  of  concrete  would  be  complete  without 
a  series  of  tests  establishing  its  strength  without  reinforcement. 

The  tests  herein  reported  indicate  that  concrete  is  unsuitable  for 
use  under  conditions  where  it  must  resist  tensile  stresses,  because 
of  the  small  loads  it  will  sustain  and  particularly  because  of  the 
suddenness  with  which  it  fails,  in  striking  contrast  to  the  behavior 
of  reinforced  concrete,  which  usually  shows  a  gradual  development 
of  cracks  preceding  failure. 

This  first  series  of  beam  tests  covers  144  beams  without  rein¬ 
forcement  8  by  11  inches  in  section  and  13  feet  long,  together  with 
the  corresponding  compression  test  pieces,  consisting  of  cylinders  8 
inches  in  diameter  by  16  inches  in  length  and  of  6-inch  cubes.  Of 
these  tests  those  on  108  beams  of  12-foot  span,  with  their  cylinders 
and  cubes,  and  those  on  108  beams  of  variable  spans,  6  to  9  feet,  which 
were  made  of  the  larger  part  of  the  13-foot  beams  after  rupture,  are 
herein  reported  and  comprise  all  of  this  series  except  the  52-week  tests. 

An  attempt  has  been  made  to  bring  out,  if  possible,  the  compara¬ 
tive  value  of  gravel,  granite,  limestone,  and  cinders  for  use  in  con¬ 
crete;  the  effect  of  age  and  consistency  on  the  strength,  as  shown  by 
the  modulus  of  rupture  of  the  long  and  short  beams  and  by  the  ulti¬ 
mate  strength  of  the  cylinders  and  cubes;  and  the  influence  of  age 
and  consistency  on  the  stiffness,  which  is  indicated  by  the  unit 

5 


6 


STRENGTH  OF  CONCRETE  BEAMS. 


elongation  of  the  long  and  short  beams  and  by  the  initial  modulus  of 
elasticity,  as  determined  by  tests  of  the  cylinders. 

Three  consistencies  —  wet,  medium,  and  damp  —  were  .  somewhat 
arbitrarily  chosen,  and  are  described  on  pages  20-21  in  greater  detail. 
Tests  were  made  at  the  ages  of  4,  13,  26,  and  52  weeks.  There  are, 
then,  as  indicated  in  the  following  table,  but  two  variables — aggre¬ 
gate  and  consistency — for  each  age. 

Outline  of  tests  of  concrete  beams. 


Consistency. 


Aggregate. 

4  weeks. 

-  .v  3 

13  weeks. 

26  weeks. 

52  weeks. 

Granite . 

Wet. 

Med. 

Damp . 

Wet. 

Med. 

Damp . 

Wet. 

Med. 

»  »  W  A  * 

Damp. 

Wet. 

Med. 

Damp. 

Gravel. . . . 

.  .do  . 

.  .do  . 

.  .do  .. . 

. .do  . 

.  .do  . 

.  .do  . . . 

. .do  . 

.  .do  . 

.  .do  . . . 

.  .do  . 

. .do  . 

.  .do  . . . 

Limestone . 

.  .do  . 

.  .do  . 

.  .do  ... 

.  .do  . 

.  .do  . 

.  .do  . . . 

.  .do  . 

.  .do  . 

.  .do  ... 

.  .do  . 

.  .do  . 

.  .do  . . . 

Cinders . 

..  - 

;.  .do  . 

.  .do  . 

..do  ... 

..do  . 

.  .  do  . 

.  .do  .. . 

.  .do  ; 

.  .do  . 

. .do  .. . 

.  .do  . 

.  .do  . 

.  .do  ... 

Note.— Three  beams,  three  cylinders,  and  three  cubes  were  made  for  each  variation  shown  in  the 
table. 


METHODS  OF  TESTING. 

The  methods  of  testing  beams  of  12-foot  and  variable  spans, 
together  with  cylinders  and  cubes,  have  been  described  in  consider¬ 
able  detail  in  Bulletin  No.  329.  It  is  thought  best,  however,  to  repeat 
and  in  some  cases  amplify  matter  which  appears  there,  as  the  intelli¬ 
gent  interpretation  of  much  of  the  test  data  is  greatly  aided  by  ready 
access  to  an  account  of  the  methods  of  testing  that  were  used. 


RESULTS  OF  TESTS. 


No  attempt  has  been  made  in  this  bulletin  to  generalize  the  results 
of  the  tests  herein  presented,  or  to  draw  any  conclusions,  however 
warranted  they  may  appear  from  an  examination  of  the  test  data. 
It  is  hoped  that  the  matter  herein  contained  will  provoke  discussion, 
and  in  order  to  promote  this  end  extended  expressions  of  opinion  or 
attempted  applications  of  theory  to  results  have  been  avoided.  A 
running  commentary  on  the  results  of  the  tests,  however,  emphasizing 
matters  of  particular  interest  and  indicating  a  few  points  that  might 
lead  to  interesting  analyses,  is  included  in  this  report.  When  the 
results  of  the  52-week  tests  become  available  it  is  the  intention  to 
publish  a  thorough  analysis  of  the  entire  series  in  another  bulletin. 

The  purpose  of  this  series  of  tests  was  to  determine — 

(1)  The  effect  of  age  on  the  strength  of  concrete; 

(2)  The  effect  of  variation  in  the  consistency  on  the  strength  of 
concrete;  and 

(3)  The  effect  of  different  types  of  aggregates  on  the  strength  of 
concrete. 

The  first  question  is  perhaps  the  most  important,  since  an  early 
attainment  of  considerable  strength  and  no  subsequent  decrease  in 


INTRODUCTION. 


7 


strength  are  two  essential  qualities  in  concrete,  in  order  that  a  struc¬ 
ture  may  be  put  to  the  use  for  which  it  is  intended  as  soon  as  possible 
and  that  there  shall  be  no  subsequent  deterioration  in  strength. 

The  least  age  at  which  any  tests  were  made  was  four  weeks,  and  at 
that  period  in  no  case  except  that  of  the  cinder  concrete,  wet  con¬ 
sistency,  did  the  compressive  strength  fall  below  2,000  pounds  per 
square  inch,  while  the  cinder  concrete  had  in  every  case  a  compressive 
strength  of  at  least  1,000  pounds  per  square  inch. 

In  every  instance  the  compressive  strength  shows  a  substantial 
increase  from  four  to  thirteen  weeks,  with  the  single  exception  of 
limestone  concrete  mixed  to  a  wet  consistency,  for  which  a  decreased 
strength  is  indicated  by  the  tests,  a  decrease  which  continues  to  the 
age  of  twenty-six  weeks.  This  decrease  in  the  strength  of  the  lime¬ 
stone  concrete  is  unexplainable,  and  the  results  of  the  52-week  tests 
on  this  material  will  be  of  value  as  indicating  whether  or  not  this 
decrease  continues  to  the  latter  period.  The  other  aggregates  show 
either  the  same  or  a  slightly  greater  strength  at  twenty-six  weeks 
than  at  thirteen  weeks. 

The  transverse  tests  on  both  the  long  and  the  short  beams  bear  out 
very  closely  the  fact  indicated  by  the  compression  tests  on  the  cylin¬ 
ders  and  cubes,  and  lead  to  the  belief  that  the  tensile  and  compressive 
strength  are  affected  alike  by  both  age  and  consistency.  The  effect 
on  the  strength  of  the  variation  in  the  consistency  is  clearly  shown. 
In  almost  every  case  the  concrete  of  the  damp  consistency  is  the 
strongest  and  that  of  the  wet  consistency  the  weakest.  This  is  true 
for  the  three  ages  at  which  the  concrete  was  tested,  and  is  confirmed 
by  the  tests  of  the  beams  as  well  as  of  the  cylinders  and  the  cubes. 
Attention  is  called  to  the  fact  that  the  damp  consistency  used  is 
much  wetter  than  the  damp  consistency  used  in  making  mortar 
building  blocks,  for  which  the  same  conclusions  may  not  apply. 

The  difference  in  strength  of  the  stone  and  gravel  concretes  of  the 
three  consistencies  is  more  pronounced  than  in  the  case  of  the  cinder 
concrete.  The  effect  of  the  consistency  on  the  strength  seems  to 
depend  to  a  great  extent  on  the  behavior  of  the  concrete  while  being 
tamped  and  to  the  method  used  in  tamping.  Great  care  was  taken 
to  tamp  all  the  concretes  in  the  same  manner.  The  thorough  mixing 
of  the  concrete  is  absolutely  essential  and  has  a  marked  influence  on 
the  consistency. 

The  relatively  slight  influence  exerted  by  the  consistency  on  the 
strength  of  cinder  concrete  may  be  partly  due  to  the  structural  weak¬ 
ness  of  the  cinders  themselves,  which  in  the  drier  mixtures  were  to  a 
great  extent  broken  up  by  the  tamper,  while  in  the  wet  mixtures,  the 
cinders  would  move  from  beneath  the  tamper. 

While  it  is  true  that  in  almost  every  instance  the  drier  mixtures 
give  the  greater  strength,  it  does  not  follow  that  dry  (or  damp) 


8 


STRENGTH  OF  CONCRETE  BEAMS. 


mixtures  should  be  used  in  construction.  Practical  considerations 
warrant  the  use  of  a  wet  mixture.  The  difficulty  in  securing  efficient 
tamping  and  a  smooth  finish  in  a  damp  concrete,  the  loss  of  strength 
due  to  the  unavoidable  drying  out  of  the  concrete  used  above  water, 
the  difficulty  of  securing  in  reinforced  concrete  an  intimate  union 
with  the  steel,  and  the  far  greater  ease  of  placing  wet  concrete  all 
seem  to  warrant  the  sacrifice  of  what  in  many  cases  is  but  a  slight 
difference  in  strength  for  a  greater  ease  of  manipulation  and  a 
thorough  bedding  of  the  steel,  which  is  of  the  utmost  importance  in 
reinforced  concrete  work. 

It  is  dangerous  to  draw  any  general  conclusions  as  to  the  relative 
value  of  concrete  made  of  the  four  aggregates  used  unless  the  char¬ 
acter  of  the  aggregates  used  in  this  particular  series  of  tests  is  care¬ 
fully  kept  in  mind.  The  gravel,  granite,  limestone,  and  cinders  were 
used  as  available  representative  types  of  aggregates,  and  while  the 
results  indicate  that  the  granite  makes  the  strongest  concrete,  it 
should  not  be  assumed,  therefore,  that  a  granite  concrete  is  stronger 
than  a  gravel,  limestone,  or  cinder  concrete.  Every  material  should 
be  accepted  or  rejected  on  the  results  of  the  tests  of  its  qualities, 
regardless  of  the  tests  of  other  materials  of  the  same  type.  Appar¬ 
ently  insignificant  differences  in  two  materials  which  appear  to  be 
similar  often  cause  considerable  difference  in  the  strength  of  concrete 
made  from  them.  For  instance,  two  limestones  from  the  same 
quarry  crushed  and  screened  under  similar  conditions — except  that 
one  was  screened  while  wet,  which  caused  the  dust  to  adhere  to  the 
surface  of  the  stone — would  make  concretes  of  considerable  difference 
in  strength. 

Because  the  hard,  flinty  gravel  used  in  these  tests  gave  excellent 
results,  it  does  not  necessarily  follow  that  a  similar  well-graded  gravel, 
but  composed  of  soft  limestone  or  shale,  would  give  like  results.  No 
series  of  investigations,  however  elaborate,  will  do  away  with  the 
necessity  of  careful  inspection  of  the  materials  to  be  used.  The  rela¬ 
tive  value  of  materials  reported  in  this  bulletin  should  be  recognized, 
therefore,  as  applicable  only  to  the  particular  materials  from  which 
the  reported  physical  properties  were  obtained. 

ACKNOWLEDGMENTS. 

All  the  material  used  in  the  tests  herein  reported  was  donated  by 
the  following  companies,  who  deserve  credit  for  their  interest  and 
hearty  cooperation  in  advancing  the  work: 

'  f"\  V  i-s  •  ■ rr>rr  r  > 

Cement. — Iola  Portland  Cement  Company,  Iola,  Kans. 

Atlas  Portland  Cement  Company,  Hannibal,  Mo. 

Whitehall  Portland  Cement  Company,  Cementon,  Pa. 

Universal  Portland  Cement  Company,  Chicago,  Ill. 

Edison  Portland  Cement  Company,  New  Village,  N.  J. 

Omega  Portland  Cement  Company,  Mosherville,  Mich. 


9 


TESTS  OF  CEMENT. 

Old  Dominion  Portland  Cement  Company,  Fordwick,  Ya. 

Lehigh  Portland  Cement  Company,  Mitchell,  Ind. 

St.  Louis  Portland  Cement  Company,  St.  Louis,  Mo. 

Sand. — Union  Sand  and  Material  Company,  St.  Louis,  Mo.  A  recent  river  sand 
dredged  from  Meramec  River  at  Drake,  Mo. 

Gravel. — Union  Sand  and  Material  Company,  St.  Louis,  Mo.  A  recent  river  gravel 
dredged  from  Meramec  River  at  Drake,  Mo. 

Granite. — Schneider  Granite  Company,  St.  Louis,  Mo.  A  hard,  red  granite  quar¬ 
ried  near  Granite ville,  Mo. 

Cinders. — United  Railways  Company,  St.  Louis,  Mo.  These  cinders  were  obtained 
from  the  Dehodiamont  power  house,  St.  Louis,  and  gave  better  results  than  those 
selected  from  other  sources. 

Limestone. — Fruin-Bambrick  Construction  Company,  St.  Louis,  Mo.  Obtained 
from  a  quarry  in  St.  Louis. 

The  tests  were  supervised  by  Louis  H.  Losse,  and  the  results  were 
computed  and  collated  by  Harry  Kaplan. 

TESTS  OF  CONSTITUENT  MATERIALS. 

CEMENT. 

PREPARATION  OF  TYPICAL  CEMENT. 

The  cement  used  in  all  the  tests  in  these  laboratories  is  known  as 
typical  Portland  cement.  It  is  prepared  by  thoroughly  mixing  to¬ 
gether  a  number  of  Portland  cements.  The  method  of  preparing  the 
typical  Portland  cement  that  was  used  in  the  tests  herein  reported  and 
in  the  tests  on  the  second  and  third  series,  reinforced  beams,  including 
in  all  576  beams,  cylinders,  and  cubes,  was  as  follows: 

One  thousand  eight  hundred  sacks  of  cement,  200  from  each  of 
nine  companies,  were  used.  Two  hundred  sacks  of  one  brand  were 
spread  over  a  concrete  floor  25  by  40  feet  in  area  and  thoroughly 
mixed  by  hoeing  from  side  to  side.  Two  samples  were  then  taken,  a 
50-pound  sample  for  tests  to  be  made  by  the  constituent-materials 
section,  and  a  smaller  one  for  chemical  tests.  The  cement  was  then 
resacked.  When  all  the  brands  had  been  separately  mixed  in  this 
way,  two  sacks  of  each  brand  were  spread  on  the  floor  in  a  layer  about 
3  inches  thick.  One  brand  was  spread  upon  another  in  blanket  form, 
making  nine  separate  layers  of  cement  for  the  nine  brands  used.  The 
mass  was  mixed  very  carefully  with  shovels  until  a  uniform  mixture 
was  obtained.  A  10-pound  sample  was  taken  for  physical  tests  and 
the  cement  was  sealed  in  air-tight  cans,  two  cans  of  800  pounds 
capacity  each  being  required  to  hold  one  mix. 

RESULTS  OF  TESTS. 

Table  1  contains  the  results  of  the  chemical  tests  of  the  individual 
brands,  made  on  samples  taken  as  indicated  above.  The  average  of 
the  columns  may  be  taken  as  the  analysis  of  the  typical  Portland 
cement. 


10  STRENGTH  OF  CONCRETE  REAMS. 


Table  1. — Chemical  analyses  of  individual  brands  used  in  the  preparation  of  typical 

Portland  cement. 


Cement  No. 

Silica 

(SiO,). 

Alumina 

(AI2O3). 

Ferric 

oxide 

(Fe203). 

Lime 

(CaO). 

Mag¬ 

nesia 

(MgO). 

Sul¬ 

phuric 

anhy¬ 

dride 

(S03). 

Water 

(H20). 

Ignition 

loss. 

Unde¬ 

ter¬ 

mined. 

200  . 

20.  34 

9.  36 

3.04 

63.  40 

1.35 

1.47 

1.04 

201 . 

22. 12 

6.  50 

3.  22 

61.39 

2.  58 

1.89 

0.94 

0. 55 

.97 

202 . 

20.96 

8.  08 

2.80 

62.  68 

1.  45 

1.54 

.18 

1.61 

.70 

203 . 

20.  52 

8.  54 

2.  68 

62.  47 

1.92 

1.50 

.29 

1.  43 

.65 

204 . 

20.  04 

7.  70 

2.  74 

63. 26 

2.  24 

1.56 

.08 

.96 

1.60 

205 . 

22.  04 

9.50 

1.42 

61.  46 . 

1.68 

1.58 

.55 

.84 

.93 

206 . . 

22.80 

9.  56 

1.06 

61.04 

1.37 

1.82 

.64 

.77 

.94 

207 . 

22.  96 

9.  34 

1.32 

61.20 

1.47 

1.81 

.28 

.86 

.76 

208 . 

23.  48 

«.  22 

1.80 

61.10 

1.62 

1.68 

.44 

.81 

.85 

Average . 

21.  70 

8.  53 

2. 23 

62.00 

1.74 

1.67 

.43 

.98 

.94 

Table  2  contains  the  results  of  the  physical  tests,  except  those  for 
strength  of  the  individual  brands.  All  these  tests  were  made  accord¬ 
ing  to  the  methods  recommended  by  the  special  committee  on  uni¬ 
form  tests  of  cement  of  the  American  Society  of  Civil  Engineers. 

Table  2. — Physical  tests  of  individual  brands  used  in  typical  Portland  cement. a 


Cement  No. 

Residue  on 
sieve  (per 
cent) — 

Specific 

gravity. 

Water 

(per 

cent). 

Time  of  set  (minutes) . 

Normal  pat  tests. 

Vicat. 

Gilmore. 

Air  (70°  F.). 

Water 
(70°  F.). 

100. 

200. 

Ini¬ 

tial. 

Final. 

Ini¬ 

tial. 

Final. 

200 . 

5  9 

20.9 

3. 136 

21.0 

184 

340 

155 

325 

Normal . 

Normal. 

201 . 

5.  5 

22. 1 

3. 058 

20.  5 

93 

378 

110 

486 

.  .do . 

Do. 

202 . 

7.8 

24.6 

3. 121 

20.  5 

138 

329 

152 

393 

.  .do . 

Do. 

203 . 

4.4 

20.6 

3.099 

21.5 

117 

315 

150 

352 

Crack  1"  long 

Do. 

from  edge. 

204 . 

2.0 

12.0 

3. 087 

24.0 

124 

416 

229 

458 

Normal 

Do. 

205 . 

6.0 

22.2 

3.165 

21.0 

127 

370 

178 

394 

W  arped  J*" 

Do. 

from  edge. 

206 . 

5.  3 

21.  5 

3. 127 

21.0 

113 

338 

195 

441 

Normal 

Do. 

207 . 

6.0 

23.2 

3. 129 

20.  5 

146 

391 

182 

372 

.  .do . 

Do. 

208 . 

3.1 

21.6 

3.141 

22.5 

170 

332 

217 

400 

. do . 

Do. 

Average. . . . 

5.1 

21.0 

3. 108 

21.4 

135 

357 

174 

402 

a  In  the  accelerated  pat  tests,  in  water  at  212°  F.  for  3  hours  and  in  steam  maintained  at  normal 
pressure  for  5  hours,  the  results  were  normal  in  each  case  for  each  brand  of  cement. 


Table  3  contains  the  results  of  the  strength  tests  of  the  indi¬ 
vidual  brands.  Tests  were  made  for  both  neat  cement  and  1 :  3  mortar 
with  Ottawa  sand,  in  tension,  compression  on  2-inch  cubes,  and 
modulus  of  rupture  on  a  1  by  1  inch  prism  tested  by  a  center  load  on 
a  12-inch  span.  All  tests  were  made  according  to  the  methods  rec¬ 
ommended  by  the  special  committee  on  uniform  tests  of  cement  of 
the  American  Society  of  Civil  Engineers. 


Strength  tests  of  individual  brands  used  in  the  preparation  of  typical  Portland  cement. 


TESTS  OF  CEMENT 


11 


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Table  3. — Strength  tests  of  individual  brands  used  in  the  preparation  of  typical  Portland  cement — Continued. 


12 


STRENGTH  OF  CONCRETE  BEAMS. 


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16 


STRENGTH  OF  CONCRETE  BEAMS. 


Table  4  contains  the  results  of  all  the  physical  tests  made  of  the 
typical  Portland  cement  that  was  used  in  the  present  series  of  con¬ 
crete  beams.  In  the  column  “  Register  No.”  is  given  the  register 
number  of  the  cement  used.  Each  number  corresponds  to  two  cans 
of  800  pounds  each  of  typical  Portland  cement.  The  sample  for 
each  test  was  taken  as  already  indicated. 

As  these  tests  were  made  with  the  sole  idea  of  checking  the  uni¬ 
formity  with  which  the  typical  Portland  cement  was  prepared,  a  full 
series  of  neat  and  sand  tests  was  thought  unnecessary  and  undesir¬ 
able,  for  it  would  entail  too  much  routine  work  on  the  part  of  the 
constituent-materials  laboratory.  Accordingly,  only  tension  tests 
on  neat  cement  were  made. 

SAND. 

The  same  sand  was  used  with  all  the  aggregates  tested.  It  is 
known  as  Meramec  River  sand,  and  is  composed  of  flint  grains  having 
comparatively  smooth  surfaces.  The  yellowish- brown  color  of  the 
flint  imparts  a  tint  of  the  same  color  to  the  sand  as  a  whole. 

Tables  5  and  6  (p.  17)  give  the  results  of  the  physical  tests  on  this 
material.  The  granulometric  analysis  in  Table  6  shows  the  sand  to 
be  rather  finer  than  desirable.  The  percentage  of  voids  was  com¬ 
puted  from  the  weight  per  cubic  foot  and  the  specific  gravity. 

Table  7  (p.  18),  which  contains  the  results  of  the  tests  made  on  the 
cement  used  in  the  preparation  of  the  test  pieces  reported  in  Table  5, 
will  aid  in  the  interpretation  of  the  values  given  in  the  latter  table. 


Table  5. —  Tests  of  mortar  made  with  Meramec  River  sand  ( Sd .  43)  and  typical  Portland  cement  ( Ct .  140)  in  concrete  beams. 


TESTS  OF  SAND 


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Cinders . 

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Fineness  of  sand. 

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a 

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« 

37206— Bull.  344—08 - 2 


18 


STRENGTH  OF  CONCRETE  BEAMS. 


AGGREGATE. 

The  results  of  the  physical  tests  on  the  granite,  gravel,  cinders,  and 
limestone  used  in  the  plain  beams  are  reported  in  Table  6.  The 
crushing  strength  of  the  1:2:4  concrete  made  of  these  aggregates  is 
given  in  connection  with  the  results  of  tests  on  the  plain  beams,  in 
Table  10  (pp.  48-53). 


Table  7. —  Tests  of  cement  140,  used  in  testing  Meramec  River  sand  ( strength  in  pounds 

per  square  inch). 


Kind  of  test. 

Neat. 

1:3  mortar. 

1  day. 

7  days. 

28 

days. 

90 

days. 

180 

days. 

360 

days. 

7 

days. 

28 

days. 

90 

days. 

T80 

days. 

360 

days. 

Tension . 

Average . 

Compression . 

Average . 

Transverse . 

362 

375 

372 

370 

3.425 

3,275 

3,300 

3, 333 

756 

792 

774 

774 

'  710 

700 
718 

709 

9,300 
9, 325 
9,175 

9,266 

1,440 

1,440 

1,476 

1,452 

696 

705 

709 

703 

10, 512 
11,125 
10, 497 

10,711 

1,872 

-1,908 

1,944 

1,908 

775 

792 

781 

.  783 

12,288 
12,612 
12, 862 

12, 590 

1,998 

2,016 

1,962 

1,992 

827 

811 

813 

817 

13, 980 
13, 725 
13, 803 

13,836 

1,944 

2,088 

2,034 

2,022 

846 

853 

831 

843 

14,274 
14, 410 
14, 320 

13, 335 

2,142 
2,232 
2, 124 

2,166 

342 

375 

364 

360 

1,570 

1,555 

1,735 

1,620 

527 

540 

531 

533 

3,200 
3, 300 
3,0^5 

3, 175 

445 

445 

413 

434 

3,698 

3,400 

3,549 

405 

388 

394 

396 

5,025 

5,025 

4,800 

4,950 

414 

408 

405 

408 

5,500 
5,  425 
5,239 

5,388 

Average . 

Remarks.-*- Fineness:  Residue  on  No.  100  sieve,  6.8  per  cent;  on  No.  200  sieve,  22.8 
per  cent.  Specific  gravity,  3.12.  Time  of  set:  Initial,  142  minutes;  final,  428 
minutes.  Soundness:  Pattest  in  air  at  70°  F.,  normal;  in  water  at  70°  F.,  normal;  in 
water  at  212°  F. ,  3  hours,  normal ;  in  steam  at  normal  pressure,  5  hours,  normal.  Water 
used  in  mixing:  Neat,  20.5  per  cent;  mortar,  8.9  per  cent.  Temperatures:  Of  air, 
71.0°  F.;  of  water,  68.0°  F. 

PREPARATION  OF  TEST  PIECES. 

METHODS  OF  PROPORTIONING. 

A  1:2:4  volume  proportion  was  adopted  for  all  the  concrete  used 
in  the  following  tests.  Since,  however,  the  volume  of  a  given  weight 
of  dry  sand  is  greatly  affected  b}7^  the  percentage  of  moisture  present, 
it  was  thought  best  to  do  the  actual  proportioning  by  weight.  The 
weight  of  1  cubic  foot  of  cement  was  assumed  to  be  100  pounds.  The 
weight  per  cubic  foot  of  the  dry,  loose  sand  and  the  dry,  loose  aggre¬ 
gate  as  determined  by  tests  in  the  constituent-materials  laboratory, 
was  used  in  reducing  the  proportions  by  volume  to  the  proportions  by 
weight. 

With  this  as  a  basis,  the  necessary  weight  of  dry  material  for  the 
desired  batch  was  determined.  Since  the  sand  and  stone,,  as  stored 
in  the  bins,  contained  an  appreciable  amount  of  moisture,  the  dry 
weight  of  the  material  had  to  be  increased  by  the  weight  of  the  mois¬ 
ture  present  before  the  batch  could  be  weighed  out.  The  percentage 
of  moisture  was  determined  on  a  500-gram  sample  of  the  sand  and 
stone  each  day  on  which  beams  were  molded. 


PREPARATION  OF  TEST  PIECES. 


19 


The  above  method  of  correcting  for  moisture  was  followed  in  the 
series  of  concrete  beams  and  in  the  greater  part  of  the  first  reinforced 
beam  series.  It  was  noticed  from  time  to  time,  however,  that  the 
concrete  when  dumped  from  the  mixer  was  not  always  of  the  same 
consistency,  in  spite  of  the  fact  that  the  total  weight  of  water  present 
(weight  of  water  added  plus  the  weight  of  the  moisture  in  the  sand  and 
the  stone)  was  a  constant.  A  moisture  determination  was  then  made 
on  a  sample  representing  as  nearly  an  average  of  the  material  in  the 
bin  as  it  was  possible  to  obtain,  and  this  was  then  maintained  constant 
and  gave  much  better  results.  The  effect  on  the  consistency  of  a  given 
change  in  the  weight  of  the  moisture  in  the  sand  or  stone  does  not 
appear  to  be  the  same  as  that  of  an  identical  change  in  the  weight  of 
the  water  added  to  the  batch,  the  difference  probably  being  due  to  the 
fact  that  the  moisture  test  is  only  local  and  does  not  represent  the 
true  average  of  the  material  in  the  bin. 

It  should  be  noted  here  that  the  proportions  by  volume  of  the  cin¬ 
der  concrete  are  nearer  1:2:5  than  1:2:4.  This  is  due  to  an  error  in 
making  the  moisture  determination  at  the  time  the  weight  per  cubic 
foot  was  determined.  The  weight  per  cubic  foot  of  the  cinders,  in¬ 
cluding  apparently  1 1 . 1  percent  moisture,  was  reported  as  68.1  pounds. 
Using  these  figures  gives  61.3  pounds  per  cubic  foot  for  the  weight  of 
the  dry,  loose  cinders.  These  determinations  were  accepted  as  cor¬ 
rect  until  a  sample,  which  had  been  forgotten  in  the  oven,  showed  23 
per  cent  moisture  present.  This  error  in  the  weight  per  cubic  foot, 
due  to  insufficient  drying  of  the  test  sample,  was  not  discovered  until 
the  series  of  cinder  beams  was  almost  completed.  While  a  new  deter¬ 
mination  of  the  weight  per  cubic  foot  was  made  and  the  proportions 
by  weight  and  volume  modified  accordingly,  it  was  thought  best  to 
use  these  proportions  and  the  correct  weight  per  cubic  foot  on  the  re- 
„  maining  cinder  beams  rather  than  the  1:2:4  volume  proportions,  in 
order  to  make  the  cinder  beams  comparable  among  themselves  even 
if  not  strictly  comparable  with  the  beams  of  other  aggregates. 

The  weight  per  cubic  foot,  as  redetermined,  was  found  to  be  47.0 
pounds. 

METHOD  OF  MIXING  AND  CONSISTENCY. 

MIXING. 

All  concrete  was  mixed  in  a  motor-driven  cubic-yard  cube  mixer, 
which  is  equipped  with  a  charging  hopper.  All  water  used  in  mixing 
concrete  was  weighed  and  was  supplied  to  the  mixer  through  a  hose 
attached  to  a  water  barrel,  which  is  mounted  on  a  platform  scale  on  a 
support  above  the  mixer.  To  insure  uniform  conditions  the  interior 
of  the  mixer  was  wetted  down  each  morning  before  the  first  mix  of 
the  day.  All  concrete  was  mixed  two  minutes  dry  and  three  minutes 


20 


STRENGTH  OF  CONCRETE  BEAMS. 


wet,  after  which  it  was  dumped  on  the  cement  floor,  shoveled  into 
wheelbarrows  and  wheeled  to  the  molding  floor.  Sufficient  material 
was  charged  into  the  mixer  to  make  two  beams,  two  cylinders,  and 
two  cubes  from  the  same  batch  of  concrete. 

CONSISTENCY. 

Definition. — The  three  consistencies,  wet,  medium,  and  damp,  as 
here  used,  represent  each  a  certain  characteristic  behavior  and  appear¬ 
ance  of  the  concrete  in  the  mixer,  on  the  floor,  and  in  the  mold  when 
subjected  to  tamping.  In  order  to  eliminate  the  personal  equation  as 
far  as  possible,  the  amount  of  water  required  to  bring  the  batch  to  a 
desired  consistency  for  a  particular  aggregate  was  carefully  deter¬ 
mined  by  trial  before  the  test  pieces  were  molded.  Thereafter  the 
weight  of  water  to  be  used  with  each  aggregate  for  that  consistency 
could  be  obtained  by  making  a  simple  correction  each  day,  depending 
upon  the  percentage  of  water  contained  in  the  aggregate  as  it  came 
from  the  bins.  The  total  amount  of  water,  including  moisture,  was 
expressed  as  a  percentage  of  the  total  weight  of  the  dry  material  and 
was  maintained  constant. 

A  brief  description  of  the  consistencies  is  given.  It  should  be  recog¬ 
nized  that  the  consistencies  as  defined  are  purely  arbitrary,  but  each, 
it  is  thought,  represents  a  characteristic  appearance  and  behavior, 
and,  with  a  little  practice,  is  readily  distinguished  from  the  others. 

Wet  consistency. — Concrete  of  wet  consistency  has  a  smooth  and 
somewhat  viscous  appearance  in  the  mixer,  or  immediately  before 
dumping.  It  flows  back  from  the  ascending  side  of  the  mixer  without 
any  tendency  toward  “breaking'7  over  at  the  top.  The  upper  sur¬ 
face  of  the  concrete  in  the  bottom  of  the  mixer  rolls  underneath  the 
mass  smoothly  and  is  carried  upward  by  adhesion  to  the  metal. 
When  dumped,  it  stands  on  the  floor  in  a  low  pile,  having  a  smooth 
surface,  and  showing  neither  voids  nor  individual  stones.  It  can  not 
be  compacted  by  tamping  in  the  molds,  but  splashes  under  the  action 
of  the  tamper.  When  finished,  water  stands  from  one-fourth  to  one- 
half  inch  deep  over  the  surface  of  the  mold. 

Medium  consistency. — Concrete  of  medium  consistency  has  a  smooth 
appearance  in  the  mixer,  but  shows  a  tendency  to  lump.  As  com¬ 
pared  to  that  of  wet  consistency  it  flows  less  smoothly  and  is  carried 
higher  by  the  ascending  side  of  the  mixer,  part  flowing  back  smoothly 
and  part  breaking  over  at  the  top  in  lumps.  When  dumped,  it  stands 
in  a  higher  pile  with  steeper  side  slopes,  exhibiting  a  somewhat  lumpy 
appearance,  and  showing  individual  sfones,  but  no  voids.  The  stones 
show  an  even  coating  of  sand  mortar.  No  water  collects  on  the  sur¬ 
face  of  the  beam  in  the  mold.  The  surface  is  easily  finished  with  a 
trowel. 


PREPARATION  OF  TEST  PIECES. 


21 


Damp  consistency . — Concrete  of  damp  consistency  is  decidedly 
granular  in  the  mixer  with  little  tendency  to  lump.  The  material  is 
carried  to  the  top  of  the  mixer  and  falls  in  individual  stones  and  frag¬ 
ments  of  mortar.  When  dumped,  it  stands  at  the  same  angle  as 
medium  concrete,  showing  both  individual  stones  and  voids.  The 
surface  of  the  pile  is  irregular.  In  the  mold  it  offers  considerable  re¬ 
sistance  to  tamping,  but  compacts  fairly  well  under  hand  tamping. 
No  water  flushes  to  the  surface  and  it  can  not  be  finished  smooth  by 
troweling. 

METHOD  OF  MOLDING. 

BEAMS. 

The  beam  molds  consisted  of  three  long  steel  channels  with  flanges 
turned  outward,  forming  the  sides  and  bottom  of  the  mold.  The  ends 
were  closed  by  short  pieces  of  channels.  The  side  and  end  pieces 
were  removable.  The  molds  were  oiled  before  the  concrete  was 
placed,  to  prevent  adhesion  to  the  surface  of  the  steel.  In  molding 
the  plain  beams  the  concrete  was  deposited  in  three  layers  of  about 
equal  thickness.  The  tamping  was  done  by  hand  with  a  13f -pound 
tamper  having  a  rectangular  head  1 J  by  3§  inches.  The  tamping  was 
started  at  one  side  of  one  end  of  the  mold  and  the  tamper  moved 
toward  the  opposite  side,  the  width  of  the  tamper  at  each  stroke. 
The  tamper  was  then  set  forward  and  the  process  repeated.  In  this 
way  each  part  of  the  layer  was  tamped  once.  The  mold  was  gone 
over  twice  in  this  way,  after  which  the  concrete  was  spaded  back  from 
the  sides  of  the  mold  and  the  layer  tamped  a  third  time.  The  same 
operation  was  followed  for  each  of  the  three  layers.  The  surface  of 
each  beam  was  finished  as  smooth  as  possible  by  troweling. 

The  side  and  end  pieces  of  the  mold  were  removed  at  the  end  of 
twenty-four  hours,  and  the  beam  was  covered  with  burlap  and  allowed 
to  remain  on  the  bottom  channel  until  moved  into  the  moist  room. 

CYLINDERS  AND  CUBES. 

In  order  to  make  the  compression  test  representative  of  the  true 
crushing  strength  of  the  concrete  in  the  beam,  the  cylinders  and 
cubes  were  molded  from  the  same  batch  as  the  beam  of  the  same 
number.  They  were  molded  in  cast-iron  separable  molds,  which  were 
oiled  previous  to  placing  the  concrete.  The  concrete  was  deposited 
in  layers  approximately  3  inches  thick,  and  each  layer  was  tamped 
twice,  a  circular  hand  tamper  3 1  inches  in  diameter  and  weighing  7 
pounds  being  used  for  the  cylinders  and  a  rectangular  tamper  3J  by  If 
inches,  weighing  13 J  pounds,  for  the  cubes. 

In  molding  the  cubes  an  effort  was  made  to  “spade”  back  the  con¬ 
crete  from  the  sides  of  the  mold,  as  was  done  in  molding  the  beams. 


22 


STRENGTH  OF  CONCRETE  BEAMS. 


The  top  surfaces  of  the  cubes  and  cylinders  were  finished  smooth  with 
a  trowel.  All  molds  were  removed  at  the  end  of  twenty-four  hours, 
and  the  test  pieces  were  marked  and  transferred  to  the  moist  room. 

MOVING  AND  STORAGE. 

The  large  number  of  beams  to  be  molded  and  the  small  space  avail¬ 
able  made  it  imperative  that  the  beams  be  moved  as  soon  as  possible. 
In  no  case  could  they  remain  where  molded  for  more  than  12  or  16 
days.  Since  a  concrete  beam  without  reinforcement,  and  weighing 
about  1,200  pounds,  has  very  little  tensile  resistance  at  this  age,  it 
was  very  important  that  they  be  handled  at  points  that  would  prevent 
any  chance  of  injury  when  being  moved  to  the  moist  room.  The 
following  plan  was  followed,  and  was  entirely  satisfactory: 

The  channel  forming  the  bottom  of  the  mold  was  placed  with  the 
flanges  turned  down.  At  the  points  where  the  beams  were  supported 
in  moving  them,  the  webs  of  the  bottom  channels  were  cut  away  for 
a  width  of  l  t\  inches.  Prior  to  molding  this  slot  was  closed  by  a  filler 
resting  on  the  uncut  flanges.  When  the  beam  was  to  be  moved,  this 
filler  was  driven  out  and  a  slightly  narrower  piece,  which  projected  1 J 
inches  beyond  each  side  of  the  beam,  was  substituted. 

A  stirrup  hanging  from  the  chain  blocks  suspended  from  trolleys 
running  on  overhead  I  beams,  was  hooked  under  these  projecting  ends 
and  lifted  a  13-foot  beam  at  two  points  8  feet  apart,  which  give  equal 
positive  and  negative  bending  moment,  and  consequently  minimum 
stresses  in  a  beam  of  that  length. 

The  beams  in  the  moist  room  were  stored  six  high,  being  supported 
at  the  same  points  as  when  brought  to  the  damp  closet. 

All  test  pieces  were  sprinkled  from  a  hose  three  times  each  day — 
at  midnight,  at  8  a.  m.,  and  at  4  p.  m. — both  before  and  after  being 
placed  in  the  moist  room. 

The  temperature  on  the  molding  floor  and  in  the  moist  room  was 
recorded  on  a  self-recording  thermometer,  and  Was  maintained  as 
near  70°  as  possible. 

METHODS  OF  TESTING. 

BEAMS. 

LONG  BEAMS. 

APPARATUS. 

PL  I  shows  a  photograph  of  a  beam  in  place.  The  supports  “P” 
for  the  beams  have  cylindrical  top  surfaces,  and  are  so  designed  as 
to  give  a  slight  yielding  motion  outward,  the  object  being  to  prevent 
any  restraint  of  the  beam  which  might  follow  from  the  lengthening 
of  the  lower  fiber. 


geological  survey 


CONCRETE  BEAM  IN  MACHINE  READY  FOR  TESTING. 


METHODS  OF  TESTING. 


23 


The  deformeter  yokes  (E,  E')  are  fastened  to  the  beam  by  tighten¬ 
ing  the  nuts  A,  which  force  the  contact  points  (b)  and  those  directly 
opposite  on  the  far  side  of  the  beam,  against  the  surface  of  the  con¬ 
crete.  The  yokes  are  equidistant  from  the  center  of  the  beam,  the 
contact  points  being  29.25  inches  apart  for  the  outer  yokes  and  24 
inches  apart  for  the  inner  set.  The  contact  points  of  the  outer  set 
were  10  inches  apart  vertically  and  those  of  the  inner  yokes  5.75 
inches  apart.  Both  yokes  were  centered  on  the  horizontal  axis  of 
the  beam,  thus  bringing  the  contact  points  of  the  outer  yokes  0.5 
inch  below  the  top  and  0.5  inch  above  the  bottom.  The  inner  yokes 
were  used  only  on  some  of  the  earlier  beams  in  order  to  test  the  con¬ 
servation  of  plane  section.  Four  pins  directly  in  line  with  the  con¬ 
tact  points  on  E  engage  cylindrical  holes  in  the  ends  of  the  four  rods? 
the  other  ends  of  which  rest  lightly  on  hard  rubber  rollers  fastened 
to  the  arms  C,  which  are  rigidly  connected  to  the  yoke  E. 

Four  micrometer  screws  reading  directly  to  0.0001  inch  work  in 
bushings  fastened  to  the  yoke  Eh  When  any  micrometer  screw  is 
brought  in  contact  with  the  end  of  the  corresponding  rod,  an  electric 
contact  is  made,  which  causes  a  click  in  the  telephone  receiver  F. 
Both  yokes  are  divided  into  two  vertical  halves  by  rubber  insulation, 
thus  making  it  possible  to  read  micrometers  on  both  sides  of  the 
beam  simultaneously. 

METHOD  OP  ZERO  DEFORMATIONS. 

The  deformation  of  concrete  in  compression  in  a  beam  is  obtained 
from  a  reading  of  the  upper  micrometers,  while  the  lower  ones  give 
the  elongation  of  concrete.  The  readings  of  both  upper  and  lower 
micrometers,  making  the  usual  assumption  of  conservation  of  plane 
section,  fix  the  position  of  the  neutral  axis.  The  beams  were  all 
tested  on  a  12-foot  span  by  two  equal  loads,  applied  at  the  third 
points  of  the  span. 

The  load  apparatus  consists  of  a  box  girder  (II)  built  of  two  6-inch 
channels  with  a  J-inch  cover  plate  on  the  top  and  the  bottom.  The 
load  is  transmitted  from  the  testing  machine  to  the  box  girder  through 
a  spherical  bearing  block  (I),  and  from  the  box  girder  to  the  beam 
by  two  2-inch  steel  rollers  (J)  bearing  on  two  steel  blocks  (not  shown) 
set  in  plaster  of  Paris.  The  upper  surface  of  these  blocks  is  a  cylin¬ 
der  of  very  large  radius  whose  axis  is  parallel  to  the  length  of  the 
beam.  With  the  exception  of  these  bearing  blocks  the  entire  load 
apparatus  is  suspended  from  the  top  head  (L)  of  the  testing  machine 
by  a  bolt  passing  through  the  spherical  bearing  block  and  engaging 
a  plate  on  the  inner  surface  of  the  box  girder.  The  steel  rollers  (J) 
are  kept  in  place  by  the  casting  which  extends  a  trifle  below  their 
axis. 


24 


STRENGTH  OF  CONCRETE  BEAMS. 


On  commencing  a  test  the  bearing  blocks  are  removed  and  yokes 
(K)  are  passed  under  the  test  beam  and  over  the  box  girder  directly 
above  the  2-inch  rollers.  The  head  (L)  is  then  run  up  until  the 
reaction  at  the  ends  of  the  test  beam  has  been  so  reduced  that  the 
total  positive  bending  moment  area  is  equal  to  the  total  negative 
bending  moment  area  within  the  gage  length,  considering  the  beam 
as  a  continuous  girder  over  four  supports,  viz,  the  two  end  supports 
and  the  two  intermediate  yokes. 

This  method  is  used  for  the  following  reason:  In  tests  of  beams  as 
usually  made,  the  upper  and  lower  fibers  of  the  beam  are  already 
deformed  and  are  under  stress  due  to  the  weight  of  the  beam  when 
the  first,  or  zero,  reading  of  the  deformeters  is  taken;  the  deforma¬ 
tions  computed  from  these  readings  are  too  small  by  an  amount 
which  becomes  relatively  more  and  more  important  as  the  breaking 
loads  decrease  and  which  in  the  case  of  plain  beams  (many  of  which 
fail  by  a  load  but  little  in  excess  of  the  weight  of  the  beam)  becomes 
a  very  large  part  of  the  ultimate  deformation. 

When  a  beam  rests  freely  on  supports,  the  upper  and  lower  fibers 
are  deformed  on  account  of  the  bending  moment  due  to  the  weight  of 
the  beam.  When  the  supports  are  at  the  ends  of  the  beam  the  upper 
fibers  are  shortened  and  the  lower  are  lengthened.  For  equal  moduli 
of  elasticity  in  tension  and  compression,  which  are  constant  for  con¬ 
crete  under  small  loads,  the  deformation  at  any  point  of  the  beam  is 
proportional  to  the  area  of  the  bending-moment  diagram  over  that 
length.  Therefore,  when  the  total  positive  bending  moment  area  in 
the  gage  length  of  the  deformeters  equals  the  total  negative  bending 
moment  area  in  the  gage  length,  the  net  total  deformation  in  that 
length  is  zero,  and  both  the  upper  and  lower  fibers  of  the  beam  have 
the  same  length  as  when  unstressed.  For  a  particular  reaction  at  the 
ends  of  the  beam  the  positive  bending  moment  area  in  the  gage 
length  is  equal  to  the  negative  bending  moment  area.  In  order  to> 
get  this  reaction  the  beams  are  supported  at  the  third  points  by  the 
head  of  the  machine  as  previously  described.  As  the  stirrups  under 
the  third  points  of  the  span  take  more  and  more  of  the  weight  of  the 
beam  the  end  reactions  become  smaller  and  smaller  and  the  character 
of  the  bending-moment  diagram  within  the  gage  length  changes 
until  the  desired  condition  is  reached. 


METHODS  OF  TESTING. 


25 


The  method  of  finding  the  required  reactions  for  total  zero  defor¬ 
mations  within  the  gage  length,  in  terms  of  the  weight  of  the  beam 
and  other  known  quantities,  may  be  understood  by  reference  to  fig.  1, 
as  follows: 


^k 

<0 

1 

1 

\ 

_ 

i 

z. 

9  - H 

z. 

L 

,  Z 

Hr 

K  s 

* - 

s 

z 

r-  s  — 

/=■ 


Tig.  1. — Diagrams  illustrating  method  for  computation  of  concrete  beams.  Upper  diagram:  Nota¬ 
tion  used.  Lower  diagram:  Curve  of  bending  moment  within  gage  length  (beam  supported  at  third 
points). 


Let  L  =  distance  between  the  supports, 
gage  length  of  deformeters. 
overhang  of  beam  at  each  end. 


or 

& 

Z 

L 

3 


—  =  distance  from  each  support  to  force  exerted  by  each  stirrup. 


W  =  total  weight  of  beam. 

—  R  =  force  exerted  by  each  stirrup  at  a  distance  of  ^  from  the 


supports. 

R  =  each  reaction  at  end. 

SS  =  any  vertical  section  within  the  gage  length  at  a  distance, 
x,  from  one  of  the  gage  points. 

Mx  =  bending  moment  at  section  SS.  . 

M0  =  bending  moment  at  deformeters,  where  x  =  0. 

O’ 

Mc  =  bending  moment  at  center  of  beam,  where  x  =  |. 


m  =  constant  bending  moment  over  the  gage  length  due  to  the 
weight  of  all  attachments,  such  as  bearing  blocks  under 
the  load  points  and  the  deformeters.  This  weight  is 
applied  outside  of  the  gage  length  and  equally  on  each 
side  of  the  center  of  the  beam. 

The  bending  moment  at  section  SS,  considering  forces  to  the  left 
only,  is  as  follows: 

-|  +  x)  +  0 - K)(j.  - f  +  *) - 2 (L  +  jizy 

■  Q  +  Z-|  +  x)2  +  m. 


26 


STRENGTH  OF  CONCRETE  BEAMS. 


Reducing  to  a  simpler  form  gives: 


-t(s+z>  4 


w 


+  m. 


The  bending  moment  at  the  end  of  the  gage  length  (x=0)  is  as 
follows : 


M0 


RL 


Wg2 


+m. 


The  bending  moment  at  the  center  of  the  gage  length 


follows : 


lVir.  = 


RL  W/L  ' 
3  4^6+Z 


+  m. 


is  as 


The  moment  diagram  between  the  third  points,  when  there  is 
both  positive  and  negative  bending  moment  in  the  gage  length,  is 
shown  in  fig.  1,  in  which  xx'  is  the  horizontal  axis  of  the  moment 
diagram.  The  curve  bee'b'  is  a  parabola  and  crosses  the  axis  at 
two  points  (viz,  e  and  e')  between  the  ends  of  the  deformeters.  Then 
in  the  gage  length  cc'  there  is  negative  bending  moment  from  c  to  e 
and  from  e'  to  c',  and  positive  bending  moment  from  e  to  e'.  The 
dotted  lines  cb,  c'b',  and  bb'  are  drawn  for  the  purpose  of  demon¬ 
stration.  Then  the  distance  Mc  represents  the  bending  moment 
at  the  center  of  the  gage  length,  and  M0  represents  the  bending 
moment  at  the  end  of  the  gage  length.  The  negative  bending- 
moment  areas  within  the  gage  length  are  cbe  and  c'b'e',  each  being 
represented  by  —  B.  The  positive  bending  moment  area  within  the 
gage  length  is  eFe'  and  is  represented  by  A. 

The  condition  that  the  positive  bending  moment  area  is  equal  to 
the  negative  bending  moment  areas  is  represented  by  the  equation 
A  =  — 2B.  Adding  the  quantity  — C  to  both  sides  of  the  equa¬ 
tion  gives  A +(  — C)  =  —  2B  — C.  The  first  part  of  this  equation 
is  the  area  included  between  the  horizontal  line  bb'  and  the  para¬ 
bola  bFb' ;  that  is,  A  +  ( —  C)  =  ^g  [Mc  +  ( —  M0)  ]. 

o 

The  second  part  of  the  equation  is  equal  to  the  area  of  the  rec¬ 
tangle  bcc'b';  that  is,  — 2B  — C  =  — gM0. 

2 

Therefore  “g  [Mc+  (  — M0)]  =  — gM0.  Whence  2MC  =  — M0. 


Methods  of  testing. 


Substituting  the  values  of  M0  and  Mc  as  found  above  gives : 

Wg2 


2RL  W AL  ,  ,  0  RL  WAL  _\  1 

3  2V_6+ZJ+2m  3  +4V6+Zy  16^ 


Whence  RL  =  +Z 


Wg2 


,16(J+Z) 


hz 


3m 


— m. 


,  „  3WAL  r7\  Wg2 

and  R  =,(  w-  +Z  )  H - ^ 

4LV-6  J  16L0+Z) 


3  in 
L  ' 


In  almost  all  the  beams  tested  at  the  laboratories  L,  Z,  g,  and  m 
are  constant.  It  only  remains  to  find  W  and  to  compute  R.  A 
table  computed  by  the  above  formula  has  been  compiled  for  all  the 
usual  values  of  W,  from  which  the  corresponding  value  of  R  in  any 
case  can  be  directly  read. 

METHOD  OF  TESTING. 


When  the  test  is  commenced,  the  top  head  is  run  up  until  the  reac¬ 
tions  causing  equal  positive  and  negative  bending  moments  over  the 
gage  length  are  developed  at  the  ends  of  the  beam.  The  sum  of  these 
reactions  will  appear  on  the  weighing  beam,  the  testing  machine 
having  been  balanced  before  the  weight  of  the  beam  and  all  test 
apparatus  comes  on  it.  A  full  set  of  deformeter  readings  is  then 
taken. 

After  the  readings  at  zero  total  deformations  in  the  gage  length 
and  when  the  beam  rests  under  its  own  weight  are  taken,  the  load  is 
applied  in  increments  of  200  to  1,000  pounds,  depending  on  the  stiff¬ 
ness  of  the  beam,  the  top  and  bottom  set  of  micrometer  readings  being 
recorded  on  the  log  sheets.  Wood  blocks  are  placed  underneath  the 
beam  during  the  test,  so  that  the  distance  it  falls  at  rupture  is  not 
more  than  one-fourth  inch. 


SHORT  BEAMS. 

The  longer  portion  of  each  beam  after  first  failure  is  again  tested 
on  as  great  a  span  as  its  length  permits,  thus  making  a  secondary 
series  of  short  beams. 

The  load  is  applied  by  the  same  apparatus  as  that  used  for  the 
long  beams,  but  instead  of  being  applied  at  the  third  points  it  is 
applied  at  points  2  feet  from  the  center  of  the  span.  The  short 
beams  are  not  suspended  for  zero  deformation  readings,  since  for  such 
small  spans  the  deformation  of  the  beam  under  its  own  weight  is  very 
small.  On  all  short  beams  the  outer  yokes  having  a  gage  length  of 
29.25  inches  are  alone  used. 


28 


STRENGTH  OF  CONCRETE  BEAMS. 


CYLINDERS  AND  CUBES. 

The  cylinders  and  cubes  are  tested  on  a  four-scre\v,  200,000-pound 
Olsen  machine.  To  insure  an  even  distribution  of  load  over  the 
entire  cross  section  the  ends  of  the  cylinders  are  bedded  in  plaster  of 
Paris  to  a  thickness  of  about  one-half  inch  on  a  piece  of  plate  glass 
(previously  oiled  to  prevent  adhesion  of  the  plaster).  The  bearing 
surfaces  are  made  normal  to  the  axis  of  the  cylinder  by  means  of  a 
spirit  level  applied  to  its  sides.  The  cubes  are  not  capped  with  plas¬ 
ter  of  Paris,  but  a  thin  piece  of  asbestos  is  placed  on  a  spherical  bear¬ 
ing  plate  when  under  test,  in  order  to  take  up  all  nonparallelism  of 
the  ends. 

The  load  is  in  each  case  carried  to  failure,  being  applied  continu¬ 
ously  to  rupture  in  the  case  of  the  cubes  and  in  increments  of  5,000 
pounds,  or  approximately  100  pounds  per  square  inch  for  the  cylin¬ 
ders.  For  each  increment  gross  deformations  are  read  on  two  oppo¬ 
site  sides  of  the  cylinder  over  a  gage  length  of  12  inches. 

RESULTS  OF  TESTS. 

9 

BEAMS  OF  CONSTANT  SPAN. 


The  detailed  results  of  the  tests  of  concrete  beams  8  by  1 1  inches 
in  section,  13  feet  long,  tested  on  a  12-foot  span  by  two  equal  loads 
applied  at  the  third  points  are  given  in  Table  8  (p.  36),  comprising  the 


I IG.  2.  Diagrams  showing  the  effect  ol  age  and  consistency  on  the  strength  of  cinder  concrete. 


RESULTS  OF  TESTS. 


29 


three  ages  of  4 ,  13,  and  26  weeks,  and  some  of  the  results  are  graph¬ 
ically  shown  in  figs.  2-5  and  10-13. 


Fig.  3.— Diagrams  showing  the  effect  of  age  and  consistency  on  the  strength  of  granite  concrete. 


The  percentage  of  water  is  expressed  in  the  table  in  terms  of  the 
total  weight  of  the  dry  material.  This  percentage  includes  the 
weight  of  the  moisture  in  the  sand  and  aggregate,  which  varies  from 


30 


STRENGTH  OF  CONCRETE  BEAMS. 


1 .5  to  2.0  per  cent  of  the  weight  of  the  stone,  from  3  to  4  per  cent  of  the 
weight  of  the  sand,  and  may  include  as  much  as  21  per  cent  of  the 
weight  of  the  cinders.  A  simple  computation,  using  the  proportions 


Fig.  5.— Diagrams  showing  the  effect  of  age  and  consistency  on  the  strength  of  limestone  concrete. 


Deformation  per  unit  of  length 

Fig.  6. — Characteristic  compression-stress  deformation  diagrams,  cinder  concrete  of  medium  consist¬ 
ency;  ages  4,  13,  and  26  weeks. 


by  weight,  will  show  that  this  21  per  cent  moisture  forms  as  much  as 
43  per  cent  of  the  total  amount  of  water,  including  moisture,  that  is 
necessary  to  bring  the  concrete  to  the  desired  consistency.  Deduct- 


RESULTS  OF  TESTS. 


31 


ing  this  43  per  cent  moisture  from  the  total  percentage  of  water 
leaves  about  12  per  cent  of  the  total  weight  of  the  dry  material  as  the 
weight  of  the  water  added  plus  the  weight  of  the  moisture  in  the 
sand.  This  does  not  differ  so  very  much  from  the  percentage  of 
water  used  for  the  other  aggregates.  As  already  indicated,  it  would 
seem  that  the  influence  of  the  water  present  in  the  stone  or  cinders  and 
even  for  usual  values  of  3  to  4  per  cent  in  the  sand  does  not  influence 
the  consistency  as  greatly 
as  does  the  same  weight 
of  water  when  added  to 
the  batch. 

Column  6  of  the  table 
gives  the  consistency  of 
the  concrete  and  must  be 
compared  with  the  defini¬ 
tions  of  wet,  medium,  and 
damp  concrete  already 
given  (p.  20). 

Columns  7,  8,  and  9 
give  the  dimensions  of  the 
beam,  the  span  being  kept 
constant  at  12  feet. 

Column  10  gives  the 
total  weight  of  the  beam, 
which  is  obtained  by 
weighing  the  beam  on  the 
testing  machine.  The  er¬ 
ror  in  weighing  is  in  no 
case  greater  than  5  pounds 
in  either  direction.  Col¬ 
umn  11  gives  the  weight 
per  cubic  foot  of  the  beam. 

Column  12  gives  the  unit 
elongation  of  the  lower 
fiber  when  the  beam  rests 
freely  on  a  12 -foot  span 
subjected  only  to  its  own  weight  and  the  weight  of  the  deformeters. 
This  value  is  obtained  by  first  taking  a  reading  for  zero  total  deforma¬ 
tion  as  already  described  (p.  23)  and  a  second  reading  when  the  beam 
rests  as  above.  This  value  is  included  for  the  reason  that  in  all  tests 
made  up  to  the  present  time  deformations  due  to  applied  load  only 
were  read.  If  it  is  desired  to  compare  the  present  tests  with  others 
already  made  the  unit  elongation  as  given  in  column  14,  which  was 
measured  at  a  load  just  previous  to  rupture,  when  decreased  by  the 


4000 


3800 


3600 


.3400 


■3200 


3000 


2800 


2600 


£  2400 


1  2200 


2000 


1800 


1600 


1400 


1200 


1000 


800 


600 


400 


200 


** 

S 

kS 

J 

y 

_ 5< 

/v 

P 

"A 

A 

./ 

A 

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/ 

/ 

?/ 

7 

wl 

V 

> 

A 

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u 

r 

if 

o 

rjr 

r 

ft 

f 

y 

rr 

r* 

/ 

i 

w 

7 

3 

T 

o 

o 

o 


o 

o 


o 

o 


Deformation  per  unit  of  length 

Fig.  7. — Characteristic  compression-stress  deformation  dia¬ 
grams,  granite  concrete  of  medium  consistency;  ages  4,  13, 
and  26  weeks. 


32 


STRENGTH  OF  CONCRETE  BEAMS. 


value  in  column  12  will  give  the  unit  elongation  at  a  point  near  rup¬ 
ture  for  the  applied  load  alone. 

Column  13  shows p43  (pounds  per  square  inch)  for  the  last  load 

previous  to  failure.  The  relation  of  this  value  to  the  breaking  value 
in  column  19  is  readily  seen  by  comparison.  In  computing  all  the 
M 

values  of  p^2  given  in  these  tables  the  nominal  values  8  inches  and  11 


inches  were  used  for  the 
breadth  (b)  and  the  depth 
(d)  of  the  beam. 

Column  14  shows  the 
unit  elongation  of  the 
lower  outer  fiber  for  the 
load  previous  to  rupture. 
An  unsuccessful  attempt 
was  made  to  obtain  an 
exact  value  for  the  unit 
elongation  of  the  lower 
fiber  at  rupture,  but  it 
was  found  impossible  to 
take  a  reading  of  the  mi¬ 
crometers  at  the  exact 
instant  of  the  breaking  of 
the  beam.  Just  previous 
to  the  break  the  concrete 
in  the  lower  fiber  elon¬ 
gates  so  rapidly  that  it  is 
impossible  to  revolve  the 
micrometer  fast  enough 
to  maintain  contact  with 
the  rod.  While  the  lower 
micrometers  on  both  sides 
of  the  beam  may  be  read 
as  the  beam  breaks  the 
values  obtained  are  so 
erratic  that  they  have 
not  been  included  in  the  tables  of  this  bulletin. 

The  unit  elongations  reported  under  “  Final  def  ormeters  ”  (columns 
13,  14,  and  15)  in  Table  8  are  the  values  obtained  at  the  last  full  set  of 
readings  preceding  the  breaking  of  the  beam,  and  it  must  therefore 
be  recognized  that  while  they  approximate  the  elongations  at  maxi¬ 
mum  load  they  are  not  absolute.  Attention  is  called  to  the  apparent 


ir> 

o 


o 

o 


o 

o 


Oeformation  per  unit  of  length 

Fig.  8. — Characteristic  compression-stress  deformation  dia¬ 
grams,  gravel  concrete  of  medium  consistency;  ages  4,  13, 
and  26  weeks. 


RESULTS  OF  TESTS. 


83 


relation  between  the  values  in  columns  13  and  14.  Separating  the 
aggregates  into  cinders  on  one  hand  and  the  three  stone  concretes  on 

M 

the  other,  the  elongation  seems  to  bear  a  direct  relation  to  or  the 

load  carried.  This  comparison,  however,  can  not  be  made  for  the 
cinders,  owing  perhaps  to  the  nonuniformity  in  the  strength  of  the 
clinker  itself. 

Column  15  shows  the  position  of  the  neutral  axis  for  the  load  pre¬ 
ceding  failure.  This  is 
obtained  from  the  usual 
assumption  of  propor¬ 
tionality  between  defor¬ 
mation  and  position  of 
the  neutral  axis. 

The  maximum  load  ap¬ 
plied  at  the  third  points 
of  the  span  (column  16) 
excludes  the  weight  of 
the  deformeters.  The 


corresponding  M ;  is 

1  bd3 

shown  in  column  17. 

Column  18  shows  the 

^  for  the  weight  of  the 

beam,  taking  into  con¬ 
sideration  the  effect  of 
the  6-inch  overhang  on 
each  end  and  also  the 
constant  weight  of  the 
deformeters. 

Column  19  shows  the 

M 
bd2’ 


4000 

3800 

3600 

3400 

3200 

3000 

2800 

2600 

-C 

O 

c 

£  2400 

C3 

=3 

Z  2200 

<o 

CL 

il  2000 

3 

o 

.5  1800 
</> 
co 
o 

1600 

c 

3  1400 
1200 
1000 

800 

600 

400 

200 


a 

7 

A 

r 

M 

/? 

/ 

7 

V 

V 

¥ 

7  w 

¥ 

\ 

to 

o 

o 

o 


o 

o 


maximum  total 

DO.' 

Oeformation  per  unit  of  length 

which  is  equal  to  the  Fig.  9. — Characteristic  compression-stress  deformation  dia- 
SUin  of  the  values  in  col-  grams,  limestone  concrete  of  medium  consistency;  ages  4,  13, 

,  and  26  weeks. 

umns  17  and  18. 

Column  20  shows  the  modulus  of  rupture  in  pounds  per  square  inch. 
These  values  were  obtained  by  multiplying  those  in  column  19  by  6. 
The  method  of  computing  the  modulus  of  rupture  should  be  empha¬ 
sized.  It  is  based  on  the  assumption  that  the  coefficients  of  elastic¬ 
ity  in  tension  and  compression  are  equal  and  constant  and  that 

37206— Bull.  344—08 - 3 


34 


STRENGTH  OF  CONCRETE  BEAMS. 


consequently  the  neutral  axis  remains  in  the  center  of  the  beam.  An 
examination  of  the  table  shows,  however,  that  the  neutral  axis 
actually  varies  from  30.4  to  63.0  per  cent  of  the  depth  of  the  beam 
below  the  top. 

Column  21  gives  the  distance  of  the  break  from  the  center  of  the 
beam,  which  in  few  cases  is  more  than  1  foot. 


RESULTS  OF  TESTS 


35 


Values  of  M-i-bd' 


P<6»  cent  of  <t 


g  S'  8  §  8  O 


Table  8. —  Tests  of  13-foot  concrete  beams  of  constant  12-foot  span . 


36 


STRENGTH  OF  CONCRETE  REAMS. 


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rH  rH  rH  • 

00  00  00 

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rH  rH  rH  • 

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05  C5  C5  • 

rH  rH  rH  • 

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05  05  05  • 

d  ^  • 

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• 

CO  CO  CO  • 

CO  co  Co  • 

CO  CO  CO  • 

rH  rH  rH  i 

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rH  rH  rH  ■ 

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rH  rH  rH  • 

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rH  rH  rH  • 

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03  03  03 

03  03  03 

03  03  03 

03  03  03 

03  03  03 

03  03 

r— 

rH  rH  , 

rH  rH  rH  , 

1 

• 

rH  rH  rH  | 

• 

rH  rH  rH  , 

rH  t-H  rH  , 

rH  t-H  t-H  | 

Tf  rf  Tf  • 

1 

• 

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1 

• 

rf  rf  -rf  • 

H  • 

Tf<  TF  Tf(  • 

^t1  ^  • 

03  03  03  ; 

03  03  03  I 

03  03  03  I 

03  03  03  i 

03  03  03 

03  03  03  i 

rH 

rH  rH  | 

rH  rH  rH  j 

rH  rH  rH  , 

rH  rH  rH  ) 

rH  rH  rH  J 

rH  rH  rH  , 

Gravel . 

. do - 

. do - 

Gravel.... 

. do - 

. do - 

Gravel _ 

. do - 

. do _ 

Limestone 

. do _ 

. do _ 

Limestone 

. do _ 

. do - 

Limestone 

. do _ 

. do _ 

91 _ 1 

92  . 

93  . 

Average 

103  . 

104  . 

105  . 

Average 

116 . 

117  . 

118  . 

Average 

131  . 

132  . 

133  . 

Average 

126 . 

127 . 

140 . 

Average 

153  . 

154  . 

155  . 

Average 

Table  8. —  Tests  of  13-foot  concrete  beams  of  constant  12-foot  span — Continued. 

TESTED  AT  TWENTY-SIX  WEEKS. 


40 


STRENGTH 

OF  CONCRETE 

BEAMS. 

- 

4 

tO  rH 

COO^P 

co  co 

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Table  9. —  Tests  of  concrete  beams  of  variable  span. 
TESTED  AT  FOUR  WEEKS. 


42 


STRENGTH 


OF  CONCRETE 


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TESTED  AT  THIRTEEN  WEEKS. 


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Table  9. —  Tests  of  concrete  beams  of  variable  span — Continued. 
TESTED  AT  TWENTY-SIX  WEEKS. 


V 


46 


STRENGTH  OF  CONCRETE  BEAMS. 


Dis¬ 

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RESULTS  OF  TESTS 


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TESTED  AT  THIRTEEN  WEEKS. 


50 


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Table  10. — Compression  tests  of  concrete  cylinders  and  cubes  accompanying  beams — Continued. 

TESTED  AT  TWENTY-SIX  WEEKS. 


52 


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a  Cylinder  did  not  break  at  3,950  unit  stress.  «  Cylinder  did  not  break  at  3,969  unit  stress.  h  Cylinder  stress  approximate. 

b  Cylinder  did  not  break  at  3,989  unit  stress.  /Cube  did  not  break  at  5,556  unit  stress.  *  Machine  vibrated  compressometer. 

c Cylinder  did  not  break  at  3,959  unit  stress.  o  Cylinder  did  not  break  at  3,978  unit  •’tress.  /Cylinder  did  not  break  at  3,858  unit  stress. 

d  Cylinder  did  not  break  at  3,979  unit  stress 


54 


STRENGTH  OF  CONCRETE  BEAMS. 


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Information  per  unit  of  length  Deformation  per  unit  of  length  Deformation  per  unit  of  length 

Fig.  11. — Characteristic  deformation  curves  for  flexure,  granite  concrete  of  medium  consistency;  ages  4,  13,  and  26  weeks. 


RESULTS  OF  TESTS. 


55 


BEAMS  OF  VARIABLE  SPAN. 


The  detailed  results  of  tests  of  the  beams  of  variable  span  are  given 
in  Table  9  (pp.  42-47),  and  some  of  the  results  are  graphically  shown 
in  figs.  2-5.  The  information  given  in  columns  1-14,  17,  18,  21,  and 
22  of  the  table  is  identical  in  character  with  that  given  in  the 
corresponding  columns  of  Table  8. 

Column  15  contains  the  unit  elongation  of  the  lower  outer  fiber 
for  the  applied  load  only,  since  the  short  beams  were  not  suspended 
for  zero  total  deformations  as  were  the  long  beams.  The  values 
of  the  unit  elongation,  including  that  due  to  the  weight  of  the  beam 
and  the  deformeters,  may  be  approximated  by  increasing  the  values 
in  column  15  by  an  amount  obtained  from  the  averages  in  column 
12,  Table  8,  on  the  assumption  that  the  elongation  is  directly  propor¬ 


tional  to  the  values  for 


M 

IxP 


which  is  approximately  true  for  values 


below  those  for  the  weight  of  the  beam  plus  the  weight  of  the  deform- 

M 

eters.  The  values  for  for  own  weight  and  deformeters  are  given 

L  A  2  o  to 


in  column  19  and,  as  may  be  seen  by  comparing  with  the  maximum 
total  values  in  column  20,  are  in  the  majority  of  cases  but  a  small 
percentage  of  the  total. 

Column  16  gives  the  position  of  the  neutral  axis  in  percentage  of 
the  depth  below  the  top  of  the  beam.  These  values  are  not  strictly 
comparable,  with  those  in  column  15,  Table  8,  since  they  are  based 
on  deformations  due  to  the  applied  load  alone. 


CYLINDERS  AND  CUBES. 


The  detailed  results  of  the  compression  tests  of  cylinders  8  inches 
in  diameter  by  16  inches  in  length  and  of  6-inch  cubes  are  given  in 
Table  10.  Some  of  the  results  are  also  graphically  shown  in  figs.  2-9. 

Columns  1-6  contain  the  same  kind  of  information  as  is  given  for 
the  beams  in  the  corresponding  columns  of  Tables  8  and  9. 

Columns  7  and  8  and  columns  13  and  14  show  the  dimensions  of  the 
cylinders  and  cubes,  respectively,  in  inches. 

Columns  9  and  15  show  the  weight  in  pounds  per  cubic  foot,  as 
figured  from  the  dimensions  and  the  actual  weight  of  each  cylinder 
and  cube  when  tested. 

Columns  10  and  16  show  the  ultimate  strength  of  each  cylinder  and 
cube  in  pounds  per  square  inch. 

The  initial  modulus  of  elasticity  (given  in  column  11)  was  obtained 
from  a  curve  showing  the  relation  between  the  unit  gross  deformation 
and  the  compressive  stress  in  pounds  per  square  inch,  by  drawing  a 
line  tangent  to  the  curve  at  the  origin  or  where  possible  coincident 
with  the  straight  line  or  initial  part  of  the  curve.  The  range  in  pounds 


56 


STRENGTH  OF  CONCRETE  BEAMS 


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Deformation  per  unit  o!  length  Deformation  per  unit  ol  length  Deformation  per  unit  o!  length 

Fig.  12.— Characteristic  deformation  curves  for  flexure,  gravel  concrete  of  medium  consistency;  ages  4,  13,  and  26  weeks. 


RESULTS  OF  TESTS.  57 

per  square  inch  within  which  the  line  drawn  coincides  with  the  curve 
is  also  shown  (column  12). 

Column  17  gives  the  ratio  of  the  ultimate  strength  of  the  cylinders 
to  that  for  the  cubes. 

It  is  to  be  regretted  that  the  capacity  of  the  machines  composing 
the  equipment  was  exceeded  by  the  strength  of  many  of  the  cylinders 
and  cubes  at  the  time  these  tests  were  made,  preventing  the  accurate 
determination  of  the  actual  growth  of  strength  with  age.  There  is, 
however,  in  almost  every  case  a  substantial  increase  in  strength 
with  age. 

The  effect  of  consistency  on  the  strength  is  much  more  noticeable, 
and  leads  to  much  more  uniform  results  for  the  cubes  and  cylinders 
than  for  the  beams.  This  would  lead  one  to  believe  that  the  effect 
of  consistency  is  much  more  noticeable  and  much  more  uniform  on 
the  compressive  strength  of  concrete  than  on  the  tensile  strength. 

Owing  to  a  breakdown  of  the  engine  it  became  necessary  to  apply 
the  load  by  hand  for  a  number  of  tests.  The  beams  and  cylinders, 
being  deemed  the  most  important,  were  tested  in  this  way,  but  because 
of  the  difficulty  of  turning  the  gears  of  the  testing  machine  by  hand 
the  testing  of  the  cubes  was  omitted. 

{  ILLUSTRATIVE  DIAGRAMS. 

Figs.  2,  3,  4,  and  5  show  graphically  the  effect  of  age  and  consistency 
on  the  ultimate  compressive  strength  of  cinder,  granite,  gravel,  and 
limestone  concretes,  as  obtained  from  the  tests  on  the  cylinders  and 
cubes  and  in  the  modulus  of  rupture  as  given  by  the  tests  in  the 
beams  of  constant  and  variable  span. 

Figs.  6,  7,  8,  and  9  show  graphically  several  characteristic  com¬ 
pression-stress  deformation  curves  obtained  from  tests  on  the  cylin¬ 
ders,  while  figs.  10,  11,  12,  and  13  show  the  deformation  curves  for  a 
few  of  the  beams  of  12-foot  span. 


58 


STRENGTH  OF  CONCRETE  REAMS 


T3 

-Q 


2 

I 

5 

o 

ifi 

3 


p  )0  JU90  J8J 


;pqH-^  jo  San|BA 


Deformation  per  gnit  of  length  Deformation  per  unit  of  length  Deformation  per  unit  of  length 

Fig.  13.— Characteristic  deformation  curves  for  flexure,  limestone  concrete  of  medium  consistency;  ages  4,  13,  and  26  weeks. 


) 


> 


SURVEY  PUBLICATIONS  ON  TESTS  OF  STRUCTURAL 

MATERIALS. 


The  following  reports,  published  by  the  Geological  Survey,  relate 
to  structural  materials,  etc. : 

Bulletin  238.  Economic  geology  of  the  Iola  quadrangle,  Kansas,  by  G.  I.  Adams, 
Erasmus  Haworth,  and  W.  R.  Crane.  1904.  8°.  83  pp.,  11  pis. 

Bulletin  243.*  Cement  materials  and  industry  of  the  United  States,  by  E.  C.  Eckel. 

1905.  8°.  395  pp.,  15  pis.  65c. 

Bulletin  260.*  The  American  cement  industry,  pp.  496-505.  1905.  40c. 

Bulletin  324.  The  San  Francisco  earthquake  and  fire  of  April  18,  1906,  and  their 
effects  on  structures  and  structural  materials,  by  G.  K.  Gilbert,  R.  L.  Humphrey, 
J.  S.  Sewell,  and  Frank  Soule.  1907.  170  pp. 

Bulletin  329.  Organization,  equipment,  and  operation  of  the  structural-materials 
testing  laboratories  at  St.  Louis,  Mo.,  by  R.  L.  Humphrey.  1908.  85  pp. 

Bulletin  331.  Portland  cement  mortars  and  their  constituent  materials;  results  of 
tests  made  at  the  structural-materials  testing  laboratories,  St.  Louis,  Mo.,  by  R.  L. 
Humphrey  and  William  Jordan,  jr.  1908.  130  pp. 

Water-Supply  Paper  143.  Experiments  on  steel-concrete  pipes  on  a  working  scale, 
by  J.  H.  Quinton.  1905.  8°.  61  pp.,  4  pis. 

Mineral  Resources  U.  S.  for  1901,*  1902,  1903,*  1904,  and  1905.*  Cement.  A 
series  of  annual  articles  on  the  cement  industry  and  the  production  of  cement 
in  the  United  States,  by  L.  L.  Kimball.  50c.  for  each  volume. 

Mineral  Resources  U.  S.  for  1906,  pp.  897-905.  Advances  in  cement  technology, 

1906,  by  E.  C.  Eckel. 

Reports  marked  with  an  asterisk  (*)  are  out  of  stock,  but  may 
be  had  from  the  Superintendent  of  Documents,  Washington,  D.  C., 
at  the  prices  named.  The  others  will  be  sent  free  to  anyone  inter¬ 
ested  on  application  to  The  Director,  United  States  Geological 
Survey,  Washington,  D.  C. 

59 

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